No frontrunner has emerged to take the BBC's £450,000-a-year job vacated by George Entwistle. Photograph: Alastair Grant/AP

A group of BBC trustees is understood to be keen to appoint an outsider as director general, although it is unclear how easy it will be to find someone willing to take the £450,000-a-year job vacated by George Entwistle without risking fresh controversy in a highly charged situation.

Tim Davie, the acting director general, was eliminated before the final shortlisting stage when he applied for the job, making a successful candidacy from him very unlikely, while Caroline Thomson, the recently departed chief operating officer, is not thought to rate her chances much after losing to Entwistle in the final stages.

Sources say some trustees believe they should look externally after Entwistle's failure, although the only known outsider on the final shortlist, Ed Richards, Ofcom's chief executive, would be controversial because he was once a policy adviser to Tony Blair and Gordon Brown.

Lord Patten, the BBC Trust chairman, indicated on Sunday that he would be keen to make an appointment "within weeks," although the trust, which met that evening, has not yet made final decisions as to how to conduct the process.

Insiders said trustees were reluctant to spend more money on headhunters – last time they spent £157,500 plus VAT hiring Egon Zehnder, whose media specialist is Dom Loehnis, a friend of David Cameron – and they wanted one round of interviews to shorten the decision making time.

Dawn Airey, a former Channel 5 chief executive, would be interested in being considered, not least because friends of hers joke that her profile is "as high as a panda's sperm count".

Now working for European broadcaster RTL, Airey would probably find the lure of the job irresistible, but she has only worked in commercial television, and is still living down her complaint that Channel 5 was about "more than just films, football and fucking". The qualifier to the quote is frequently forgotten, and Airey is often cited as a source for a so-called "three Fs" onscreen strategy.

David Abraham, Channel 4's chief executive, was also being touted as a potential director general on Monday, but he is understood to be almost certainly ruling himself out. Allies say he has long been sceptical of the BBC's complex two-tier governance system. By contrast the state-owned Channel 4 is regulated by Ofcom and run by a conventional corporate board, although not for profit.

Complicating the recruitment picture is Patten's desire for a management overhaul of the BBC, in which he has talked broadly about separating the director general's dual role of running the organisation and being chief editor.

That would, to some degree, mirror the structure from Mark Thompson's earlier period as director general, in which Mark Byford, his deputy, had overall responsibility for journalism – and for dealing with editorial crises such as those that have engulfed Newsnight.

The dozen making the choice

Six women and six men, including Lord Patten, make up the BBC Trust, the body charged with choosing another director general of the BBC so soon after the disastrous decision to appoint George Entwistle.

The varied group has only a handful of heavyweight figures, with ITV's former director of programmes, David Liddiment, one of the most influential voices because he has senior broadcasting experience. He chairs the audience and performance committee, which reviews the BBC's vast output.

Liddiment is close to Alison Hastings, a former editor of the Newcastle Evening Chronicle who later sat on the Press Complaints Commission and is now a media consultant based in Liverpool. She chairs the editorial standards committee, whose job it is to handle the most serious complaints that are referred up from the BBC.

Much travelled investment banker Anthony Fry, who has worked at Rothschild, Credit Suisse and Lehman Brothers, chairs the trust's powerful finance committee, which monitors the BBC's £5bn budget. But few others are taken seriously in a body otherwise dominated by Patten, the former Conservative party chairman.

The trust's vice chair is the cerebral Diane Coyle, normally quiet at trust meetings, a former journalist and competition commissioner, who is married to the BBC's technology correspondent, Rory Cellan-Jones.

• This article was amended on 12 November 2012. The original said Alison Hastings was understood to be leading a group of BBC trustees who were keen to appoint an outsider as director general. Hastings contacted us after publication to say that is not the case.